The millimeter/submillimeter spectrum of 1H-1,2,4-triazole is reported from 70 to 700 GHz, providing spectral frequencies directly comparable to radio telescopes and enabling an astronomical search. Using four deuteriated samples of 1,2,4-triazole, we measured, assigned, and least-squares fit transitions for 26 isotopologues to sextic A- and S-reduced Hamiltonians. An accurate and precise semi-experimental (reSE) structure from 50 independent moments of inertia has been obtained. Structural parameters are provided with 2σ uncertainties within 0.0009 Å for bond distances and 0.09° for bond angles. The structural parameters are in quite good agreement with the best theoretical estimate (BTE) obtained using CCSD(T)/cc-pCV5Z, where an agreement within the 2σ uncertainty is observed for all but one case. Despite the large number of isotopologues already included in this structure, more may be useful. One isotopologue, [1,3-2H]-1H-1,2,4-triazole, is observed to closely approach the oblate asymmetric-top limit, resulting in a clear breakdown of the A-reduction Hamiltonian. The highly accurate reSE structure and subsequent analysis demonstrates that the S-reduction is also unable to adequately model the spectrum of this isotopologue.